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A233999
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Values of n such that numbers of the form x^2+n*y^2 for some integers x, y cannot have prime factor of 7 raised to an odd power.
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3
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1, 2, 4, 8, 9, 11, 15, 16, 18, 22, 23, 25, 29, 30, 32, 36, 37, 39, 43, 44, 46, 49, 50, 51, 53, 57, 58, 60, 64, 65, 67, 71, 72, 74, 78, 79, 81, 85, 86, 88, 92, 93, 95, 98, 99, 100, 102, 106, 107, 109, 113, 114, 116, 120, 121, 123, 127, 128, 130, 134, 135, 137, 141, 142, 144, 148, 149
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OFFSET
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1,2
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COMMENTS
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Equivalently, numbers of the form 49^n*(7m+1), 49^n*(7m+2), or 49^n*(7m+4). [Corrected by Charles R Greathouse IV, Jan 12 2017]
Numbers whose squarefree part is congruent to a (nonzero) quadratic residue modulo 7.
The integers in a subgroup of the positive rationals under multiplication. As such the sequence is closed under multiplication and - where the result is an integer - under division. The subgroup has index 4 and is generated by the primes congruent to a quadratic residue (1, 2 or 4) modulo 7, the square of 7, and 3 times the other primes; that is a generator corresponding to each prime: 2, 3*3, 3*5, 7^2, 11, 3*13, 3*17, 3*19, 23, 29, 3*31, ... .
(End)
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LINKS
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FORMULA
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PROG
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(PARI) list(lim)=my(v=List(), t, u); forstep(k=1, lim\=1, [1, 2, 4], listput(v, k)); for(e=1, logint(lim, 49), u=49^e; for(i=1, #v, t=u*v[i]; if(t>lim, break); listput(v, t))); Set(v) \\ Charles R Greathouse IV, Jan 12 2017
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CROSSREFS
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First differs from A047350 by including 49.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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